3.99: Tangent to exponential curve

A curve has equation $y = 5\mathrm{e}^{x} + \mathrm{e}^{-2x}$. The tangent at $x = 1$ cuts the $x$-axis at $P$. Find the equation of the tangent in the form $y = mx + c$ and hence the $x$-coordinate of $P$.